Is GPU the future of Scientific Computing ?
Georges-Henri Cottet; Jean-Matthieu Etancelin; Franck Perignon; Christophe Picard; Florian De Vuyst; Christophe Labourdette
Annales Mathématiques Blaise Pascal, Volume 20 (2013) no. 1, p. 75-99

These past few years, new types of computational architectures based on graphics processors have emerged. These technologies provide important computational resources at low cost and low energy consumption. Lots of developments have been done around GPU and many tools and libraries are now available to implement efficiently softwares on those architectures.

This article contains the two contributions of the mini-symposium about GPU organized by Loïc Gouarin (Laboratoire de Mathématiques d’Orsay), Alexis Hérault (CNAM) and Violaine Louvet (Institut Camille Jordan). This mini-symposium was an opportunity to explore the upcoming role of hardware accelerators and how it will affect the way applications are designed and developed.

As the main issue of the mini-symposium was graphical cards, this document contains contributions about two feedbacks on the behavior of different numerical methods on GPU:

  • ones on particle method for transport equations,
  • the other on Lattice Boltzmann Methods for Navier–Stokes equations, Finite Volume schemes for Euler equations and particles methods for kinetic equations.

Ces dernières années, de nouveaux types d’architectures basés sur les processeurs graphiques ont émergés. Ces technologies fournissent d’importantes ressources computationelles à faible coût et faible consommation d’énergie. Les nombreux dévelopements effectués sur le GPU ont alors permis la création et l’implémentation de logiciels sur ce type d’architecture.

Cet article contient les deux contributions de ce mini-symposium GPU organisé par Loïc Gouarin (Laboratoire de Mathématiques d’Orsay), Alexis Hérault (CNAM) et Violaine Louvet (Institut Camille Jordan). La premiere concerne les méthodes particulaires pour les équations de transport, la seconde concerne la résolution des équations de Navier-Stokes et des équations d’Euler.

Classification:  35L05,  65M08,  76M25,  76N15,  76P05,  97N40
Keywords: GPU, méthode particulaire, EDP, Mécanique des Fluides, interaction, visualisation, calcul instantané, volumes finis, méthode Lattice Boltzmann, méthode particulaire, programmation multicœur
     author = {Cottet, Georges-Henri and Etancelin, Jean-Matthieu and Perignon, Franck and Picard, Christophe and De Vuyst, Florian and Labourdette, Christophe},
     title = {Is GPU the future of Scientific Computing ?},
     journal = {Annales Math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {20},
     number = {1},
     year = {2013},
     pages = {75-99},
     doi = {10.5802/ambp.322},
     mrnumber = {3112240},
     zbl = {1296.68027},
     language = {en},
     url = {}
Cottet, Georges-Henri; Etancelin, Jean-Matthieu; Perignon, Franck; Picard, Christophe; De Vuyst, Florian; Labourdette, Christophe. Is GPU the future of Scientific Computing ?. Annales Mathématiques Blaise Pascal, Volume 20 (2013) no. 1, pp. 75-99. doi : 10.5802/ambp.322.

[1] M. Bergdorf; P. Koumoutsakos A Lagrangian particle-wavelet method, Multiscale Models. Simul., Tome 5 (2006) no. 3, pp. 980-995 | Article | MR 2272307 | Zbl 1122.65085

[2] R.A. Brownlee; A.N. Gorban; J. Levesley Stabilization of the lattice Boltzmann method using the Ehrenfests’ coarse-graining data, Physical Review E, Tome 74 (2006), pp. 037703 | Article

[3] Carlo Cercignani The Boltzmann Equation and Its Applications, Springer-Verlag Tome 67 (1988) | MR 1313028 | Zbl 0646.76001

[4] E. Godlewski; P.-A. Raviart Numerical approximation of hyperbolic conservation laws, Applied Mathematical Sciences, Springer-Verlag, Boston Tome 118 (1996) | MR 1410987

[5] D. Hanel; R. Schwane An implicit Flux-Vector Splitting Scheme for the computation of viscous hypersonic flow, AIAA Paper, Tome 25 (1989) (Paper 89-0274)

[6] A. Harten; P.D. Lax; B. van Leer On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review, Tome 25 (1983), pp. 35-61 | Article | MR 693713 | Zbl 0565.65051

[7] A. Magni; G.H. Cottet Accurate, non-oscillatory, remeshing schemes for particle methods, J. Comput. Phys., Tome 231 (2012) no. 1, pp. 152-172 | Article | MR 2846992 | Zbl pre06044227

[8] A. Munshi The OpenCL Specification, Khronos OpenCL Working Group (2011)

[9] RR. Nourgaliev; T.N. Dinh; T.G. Theofanous; D. Joseph The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. of Multiphase Flow, Tome 29 (2003), pp. 117-169 | Article | Zbl 1136.76594

[10] CUDA C Best Practices Guide 4.1, NVIDIA (2012)

[11] D. Rossinelli; M. Bergdorf; G.H. Cottet; P. Koumoutsakos GPU accelerated simulations of bluff body flows using vortex methods, J. Comput. Phys., Tome 229 (2010) no. 9, pp. 3316-3333 | Article | MR 2601102 | Zbl pre05693261

[12] Sauro Succi The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford (2001) (ISBN:0-19-850398-9) | MR 1857912 | Zbl 0990.76001

[13] F. De Vuyst A Flux Vector Splitting method that preserves stationary contact discontinuities, Acta Mathematicae Applicandae (2013) (accepted, under revision)

[14] F. De Vuyst; F. Salvarani GPU-Accelerated numerical simulations of the Knudsen gas on time-dependent domains, Computer Physics Communications, Tome 184 (2013) no. 3, pp. 532-536 | Article | MR 3007037